基于拓扑优化的噪声频率响应函数用于损伤识别
Damage identification using noisy frequency response functions based on topology optimization
AI总结：
本文提出了一种利用噪声频率响应函数和拓扑优化的鲁棒损伤识别方法，通过最小化实验模态分析与有限元分析得到的频率响应函数误差，识别结构损伤拓扑。
摘要：
本文提出了一种利用噪声频率响应函数和拓扑优化的鲁棒损伤识别方法。将损伤识别问题视为从结构的测得动态响应中生成损伤拓扑的反问题。方法基于最小化表示测得频率响应函数与谐波响应分析得到的频率响应函数误差的目标函数。在最小化过程中，通过改变材料分布或结构拓扑，将最优损伤拓扑识别为未分配材料的区域，使用固有材料与惩罚（SIMP）进行优化。为克服反问题的病态问题，提出应用最小绝对收缩和选择运算符（Lasso）正则化或对设计变量的L1范数进行惩罚。应用Lasso正则化可消除虚假损伤区域并减小测量噪声的影响。本文首先介绍了所提出方法的数学背景及其数值实现，并将其应用于悬臂板的损伤识别。实验获得频率响应函数并应用所提方法，证明该方法能成功识别损伤。
英文摘要：
This paper proposes a robust damage identification method using noisy frequency response functions (FRFs) and topology optimization. We formulate the damage identification problem as an inverse problem of generating the damage topology of the structure from measured dynamic responses of the structure to given external dynamic loading. The method is based on the minimization of the objective function representing errors between measured FRFs of the structure obtained by experimental modal analysis, and those obtained by harmonic response analysis using finite element analysis. In the minimization process, material distribution, or the topology of the structure is varied and the optimal damage topology is identified as regions with no material assigned as a result of the minimization using the solid isotropic material with penalization (SIMP). In order to overcome the problems caused by the ill-posedness of the inverse problem, it is proposed that the least absolute shrinkage and selection operator (Lasso) regularization, or the penalization to the L1 norm of the design variable be applied to the original objective function. By applying Lasso regularization, the method is expected not only to eliminate spurious damaged regions but also to minimize the effect of measurement noises. This paper first presents the mathematical background and its numerical implementation of the proposed methodology. The method is then applied to the identification of a damage of cantilevered plates. The FRFs were experimentally obtained and the proposed method is applied. It is shown that the method successfully identifies the damage.
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